Acknowledgements

Estimating climate impacts

An excellent review is Blanc and Reilly (2017). There are three broad approaches:

Mendelsohn, Nordhaus, and Shaw (1994)

Schlenker and Roberts (2009)

Data

Naive matching

Treatment effect: \(E[Y|X, T = 1] - E[Y|X, T = 0]\). But this is not an RCT. Matching provides a method of balancing \(X\) between treatment and control groups. If \(c(i)\) is the control that minimizes \(d(X_i, X_{c(i)})\) for some distance metric \(d\), then a pair matching estimator is

\[\hat{\tau}_{1p} = \frac{1}{N_1} \sum \limits_{i \in N_1} (Y_{i,1} - Y_{c(i), 0}),\]

where \(Y_{i,1}\) is the treated observation and \(Y_{c(i),0}\) is the matched control observation.

There be dragons

Problem: But here \(Y_{i,1}\) is unobserved while \(Y_{i,0}\) is observed…

Solution: Estimate \(Y_{i,1}\) by matching the treatment characteristics \(T_i\) to the closest treatment characteristics in the control, i.e. choose \(c(i) = \mbox{argmin}_{c(i)} \; d(T_i, T_{c(i)})\), in which case the estimator is

\[\hat{\tau}_{1p} = \frac{1}{N_1} \sum \limits_{i \in N_1} (Y_{c(i),0} - Y_{i, 0}).\]

\(T_i\) here is not a dummy. It’s a vector of continuous climate variables. Other predictors of \(Y_{i,1}\) such as random forests may be better…

Distance metrics

Issue 1: Multiple causal mechanisms

Issue 2: How good are the matches?

References

Antle, John M., and Claudio O. Stöckle. 2017. “Climate Impacts on Agriculture: Insights from Agronomic-Economic Analysis.” Review of Environmental Economics and Policy 11 (2). Oxford University Press (OUP): 299–318. doi:10.1093/reep/rex012.

Blanc, Elodie, and John Reilly. 2017. “Approaches to Assessing Climate Change Impacts on Agriculture: An Overview of the Debate.” Review of Environmental Economics and Policy 11 (2). Oxford University Press (OUP): 247–57. doi:10.1093/reep/rex011.

Mendelsohn, Robert, William D Nordhaus, and Daigee Shaw. 1994. “The Impact of Global Warming on Agriculture: A Ricardian Analysis.” The American Economic Review. JSTOR, 753–71.

Schlenker, W., and M. J. Roberts. 2009. “Nonlinear Temperature Effects Indicate Severe Damages to U.s. Crop Yields Under Climate Change.” Proceedings of the National Academy of Sciences 106 (37). Proceedings of the National Academy of Sciences: 15594–8. doi:10.1073/pnas.0906865106.

Sekhon, Jasjeet S. 2011. “Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching Package for R.” Journal of Statistical Software 42 (7): 1–52.